There is a huge amount of variation in Aspies that it is pretty hard to narrow down a few careers that would work well.
I like the idea of teaching because I tend to be pedantic by nature, but if I were to teach children, they would probably have me tied up, gagged and thrown into a corner before the end of the first day. (I don't know how to deal with children). But teaching adults who were interested in the subject, photography for example, could be interesting.
I would guess if an Aspie wanted to do professional sports, it would be best to favor ones that don't require as much team work. I enjoy cycling because I am only competing with myself.
My guess is that the best work for an Aspie is that which allows you to concentrate for long periods of time without interruption from others. My skills are mostly in visual things so my work of motion graphics and still photo retouching as well as some photography is ideal for my personality. I get an assignment to create an animation or retouch a photo and then I go off and do the work alone, showing my progress along the way. One thing that drives me nuts is when my boss wants to sit with me while I work on an animation.
Computer programming is another field that demands long periods of concentration.
Some people also enjoy data entry work. While intellectually boring, this kind of work, for the right person, can leave your mind free to wander and allows you to use your creative energy for your interests outside of work.
Janitorial or stocking work can be appealing for the same reasons. I spent 9 years working as a movie theatre projectionist because it gave me a great deal of free time to write or read or otherwise do stuff between threading and starting projectors. It won't pay well, but if it pays enough for you to survive and be happy, that's all that matters.
There are trade offs in any career choice. In mine, the work can dry up quickly and I have to scramble to make enough to survive. My father worked as an engineer for the government which was a safe job, but very limited in terms of his freedom to do what he chose. My brother is a research scientist with a pharmaceutical company and is quite successful, but works insanely long hours.
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Never let the weeds get higher than the garden,
Always keep a sapphire in your mind.
(Tom Waits "Get Behind the Mule")